{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "13d83b59-57f7-48ee-8bff-deda7d28edc5",
   "metadata": {
    "tags": []
   },
   "source": [
    "\n",
    "# Min Graph Coloring Problem\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d56bb6d-9f3b-45db-8e98-b50f27af7505",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "lines_to_next_cell": 2,
    "tags": []
   },
   "source": [
    "\n",
    "## Background\n",
    "\n",
    "Given a graph $G = (V,E)$, find the minimal number of colors k\u2000required to properly color it.\n",
    "A coloring is legal if:\n",
    "\n",
    "- each vetrex ${v_i}$ is assigned with a color $k_i \\in \\{0, 1, ..., k-1\\}$\n",
    "- adajecnt vertex have different colors: for each $v_i, v_j$ such that $(v_i, v_j) \\in E$, $k_i \\neq k_j$.\n",
    "A graph which is k-colorable but not (k\u22121)-colorable is said to have chromatic number k. The maximum bound on the chromatic number is $D_G + 1$, where $D_G$ is the maximum vertex degree. The graph coloring problem is known to be in the NP-hard complexity class."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bdc4e6a-199b-44b3-bd3f-fd24722b616b",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Solving the problem with classiq\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5eeb0034-b0e0-4aa4-93f5-7172437c5cdd",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Define the optimization problem\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b80625e0-9c9c-4ed2-9109-0493521ac310",
   "metadata": {},
   "source": [
    "We encode the graph coloring with a matrix of variables `X` with dimensions $k \\times |V|$ using one-hot encoding, such that a $X_{ki} = 1$ means that vertex i is colored by color k.\n",
    "\n",
    "We require that each vertex is colored by exactly one color and that 2 adjacent vertices have different colors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "83ddbd07-f7ab-4d80-b357-3890622d395f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:30.726956Z",
     "iopub.status.busy": "2024-05-07T15:52:30.726492Z",
     "iopub.status.idle": "2024-05-07T15:52:31.138614Z",
     "shell.execute_reply": "2024-05-07T15:52:31.137980Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "import pyomo.environ as pyo\n",
    "\n",
    "\n",
    "def define_min_graph_coloring_model(graph, max_num_colors):\n",
    "    model = pyo.ConcreteModel()\n",
    "\n",
    "    nodes = list(graph.nodes())\n",
    "    colors = range(0, max_num_colors)\n",
    "\n",
    "    model.x = pyo.Var(colors, nodes, domain=pyo.Binary)\n",
    "    x_variables = np.array(list(model.x.values()))\n",
    "\n",
    "    adjacency_matrix = nx.convert_matrix.to_numpy_array(graph, nonedge=0)\n",
    "    adjacency_matrix_block_diagonal = np.kron(np.eye(degree_max), adjacency_matrix)\n",
    "\n",
    "    model.conflicting_color_constraint = pyo.Constraint(\n",
    "        expr=x_variables @ adjacency_matrix_block_diagonal @ x_variables == 0\n",
    "    )\n",
    "\n",
    "    @model.Constraint(nodes)\n",
    "    def each_vertex_is_colored(model, node):\n",
    "        return sum(model.x[color, node] for color in colors) == 1\n",
    "\n",
    "    def is_color_used(color):\n",
    "        is_color_not_used = np.prod([(1 - model.x[color, node]) for node in nodes])\n",
    "        return 1 - is_color_not_used\n",
    "\n",
    "    # minimize the number of colors in use\n",
    "    model.value = pyo.Objective(\n",
    "        expr=sum(is_color_used(color) for color in colors), sense=pyo.minimize\n",
    "    )\n",
    "\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3496c5d6-7df6-49fb-b5b9-5ba48d2b7d62",
   "metadata": {},
   "source": [
    "### Initialize the model with example graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bc9871c1-224e-4206-b39e-af7e448aca70",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:31.141813Z",
     "iopub.status.busy": "2024-05-07T15:52:31.141172Z",
     "iopub.status.idle": "2024-05-07T15:52:31.697290Z",
     "shell.execute_reply": "2024-05-07T15:52:31.696530Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph = nx.erdos_renyi_graph(5, 0.3, seed=79)\n",
    "nx.draw_kamada_kawai(graph, with_labels=True)\n",
    "\n",
    "degree_sequence = sorted((d for n, d in graph.degree()), reverse=True)\n",
    "degree_max = max(degree_sequence)\n",
    "max_num_colors = degree_max\n",
    "\n",
    "coloring_model = define_min_graph_coloring_model(graph, max_num_colors)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "958deac9-b057-485e-bea0-52b95664ae6b",
   "metadata": {},
   "source": [
    "### show the resulting pyomo model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e5ba50c9-5d89-4ebf-9475-830da3ce5539",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:31.700521Z",
     "iopub.status.busy": "2024-05-07T15:52:31.699501Z",
     "iopub.status.idle": "2024-05-07T15:52:31.706355Z",
     "shell.execute_reply": "2024-05-07T15:52:31.705805Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 Set Declarations\n",
      "    each_vertex_is_colored_index : Size=1, Index=None, Ordered=Insertion\n",
      "        Key  : Dimen : Domain : Size : Members\n",
      "        None :     1 :    Any :    5 : {0, 1, 2, 3, 4}\n",
      "    x_index : Size=1, Index=None, Ordered=True\n",
      "        Key  : Dimen : Domain              : Size : Members\n",
      "        None :     2 : x_index_0*x_index_1 :   15 : {(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 2), (2, 3), (2, 4)}\n",
      "    x_index_0 : Size=1, Index=None, Ordered=Insertion\n",
      "        Key  : Dimen : Domain : Size : Members\n",
      "        None :     1 :    Any :    3 : {0, 1, 2}\n",
      "    x_index_1 : Size=1, Index=None, Ordered=Insertion\n",
      "        Key  : Dimen : Domain : Size : Members\n",
      "        None :     1 :    Any :    5 : {0, 1, 2, 3, 4}\n",
      "\n",
      "1 Var Declarations\n",
      "    x : Size=15, Index=x_index\n",
      "        Key    : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "        (0, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "        (2, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "        (2, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "        (2, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "        (2, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "        (2, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "\n",
      "1 Objective Declarations\n",
      "    value : Size=1, Index=None, Active=True\n",
      "        Key  : Active : Sense    : Expression\n",
      "        None :   True : minimize : 1 - (1 - x[0,0])*(1 - x[0,1])*(1 - x[0,2])*(1 - x[0,3])*(1 - x[0,4]) + 1 - (1 - x[1,0])*(1 - x[1,1])*(1 - x[1,2])*(1 - x[1,3])*(1 - x[1,4]) + 1 - (1 - x[2,0])*(1 - x[2,1])*(1 - x[2,2])*(1 - x[2,3])*(1 - x[2,4])\n",
      "\n",
      "2 Constraint Declarations\n",
      "    conflicting_color_constraint : Size=1, Index=None, Active=True\n",
      "        Key  : Lower : Body                                                                                                                                                                                                                                                                                                                                                                                                   : Upper : Active\n",
      "        None :   0.0 : (x[0,1] + x[0,3] + x[0,4])*x[0,0] + (x[0,0] + x[0,3])*x[0,1] + x[0,3]*x[0,2] + (x[0,0] + x[0,1] + x[0,2])*x[0,3] + x[0,0]*x[0,4] + (x[1,1] + x[1,3] + x[1,4])*x[1,0] + (x[1,0] + x[1,3])*x[1,1] + x[1,3]*x[1,2] + (x[1,0] + x[1,1] + x[1,2])*x[1,3] + x[1,0]*x[1,4] + (x[2,1] + x[2,3] + x[2,4])*x[2,0] + (x[2,0] + x[2,3])*x[2,1] + x[2,3]*x[2,2] + (x[2,0] + x[2,1] + x[2,2])*x[2,3] + x[2,0]*x[2,4] :   0.0 :   True\n",
      "    each_vertex_is_colored : Size=5, Index=each_vertex_is_colored_index, Active=True\n",
      "        Key : Lower : Body                     : Upper : Active\n",
      "          0 :   1.0 : x[0,0] + x[1,0] + x[2,0] :   1.0 :   True\n",
      "          1 :   1.0 : x[0,1] + x[1,1] + x[2,1] :   1.0 :   True\n",
      "          2 :   1.0 : x[0,2] + x[1,2] + x[2,2] :   1.0 :   True\n",
      "          3 :   1.0 : x[0,3] + x[1,3] + x[2,3] :   1.0 :   True\n",
      "          4 :   1.0 : x[0,4] + x[1,4] + x[2,4] :   1.0 :   True\n",
      "\n",
      "8 Declarations: x_index_0 x_index_1 x_index x conflicting_color_constraint each_vertex_is_colored_index each_vertex_is_colored value\n"
     ]
    }
   ],
   "source": [
    "coloring_model.pprint()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fed74b17-0343-410f-b061-f4f8e422c3ab",
   "metadata": {},
   "source": [
    "### Initialize classiq QAOA solver"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccba58ac-beef-47cd-8e55-fa84d652eb65",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Setting Up the Classiq Problem Instance\n",
    "\n",
    "In order to solve the Pyomo model defined above, we use the Classiq combinatorial optimization engine. For the quantum part of the QAOA algorithm (`QAOAConfig`) - define the number of repetitions (`num_layers`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bcf6b25c-d91a-418d-9de7-9bfbe5d8a42a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:31.708858Z",
     "iopub.status.busy": "2024-05-07T15:52:31.708376Z",
     "iopub.status.idle": "2024-05-07T15:52:33.883015Z",
     "shell.execute_reply": "2024-05-07T15:52:33.882200Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from classiq import construct_combinatorial_optimization_model\n",
    "from classiq.applications.combinatorial_optimization import OptimizerConfig, QAOAConfig\n",
    "\n",
    "qaoa_config = QAOAConfig(num_layers=6, penalty_energy=10.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7de6b8d-bb0e-4d01-9259-59340b2f1e83",
   "metadata": {},
   "source": [
    "For the classical optimization part of the QAOA algorithm we define the maximum number of classical iterations (`max_iteration`) and the $\\alpha$-parameter (`alpha_cvar`) for running CVaR-QAOA, an improved variation of the QAOA algorithm [[3](#cvar)]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "37b4ee2f-3be3-4431-961b-83f7daa619fb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:33.888302Z",
     "iopub.status.busy": "2024-05-07T15:52:33.886923Z",
     "iopub.status.idle": "2024-05-07T15:52:33.893699Z",
     "shell.execute_reply": "2024-05-07T15:52:33.892867Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "optimizer_config = OptimizerConfig(alpha_cvar=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "beb4daac-5567-4d30-9f7a-2c7255807f85",
   "metadata": {},
   "source": [
    "Lastly, we load the model, based on the problem and algorithm parameters, which we can use to solve the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "94aa17c5-439d-4dc6-9470-74993d9c9fd5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:33.898244Z",
     "iopub.status.busy": "2024-05-07T15:52:33.897051Z",
     "iopub.status.idle": "2024-05-07T15:52:36.640923Z",
     "shell.execute_reply": "2024-05-07T15:52:36.639960Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "qmod = construct_combinatorial_optimization_model(\n",
    "    pyo_model=coloring_model,\n",
    "    qaoa_config=qaoa_config,\n",
    "    optimizer_config=optimizer_config,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7433de86-94d3-4ab2-96d8-c6e22f8f7133",
   "metadata": {},
   "source": [
    "We also set the quantum backend we want to execute on:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a7d86d74-2f1c-49c4-af90-878295ceb55b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:36.645399Z",
     "iopub.status.busy": "2024-05-07T15:52:36.645005Z",
     "iopub.status.idle": "2024-05-07T15:52:37.189978Z",
     "shell.execute_reply": "2024-05-07T15:52:37.189309Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from classiq import set_execution_preferences\n",
    "from classiq.execution import ClassiqBackendPreferences, ExecutionPreferences\n",
    "\n",
    "backend_preferences = ExecutionPreferences(\n",
    "    backend_preferences=ClassiqBackendPreferences(backend_name=\"aer_simulator\")\n",
    ")\n",
    "\n",
    "qmod = set_execution_preferences(qmod, backend_preferences)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "17ed6f20-f1e7-4305-86ad-91f3e6939e0b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:37.194561Z",
     "iopub.status.busy": "2024-05-07T15:52:37.193386Z",
     "iopub.status.idle": "2024-05-07T15:52:37.824276Z",
     "shell.execute_reply": "2024-05-07T15:52:37.823525Z"
    }
   },
   "outputs": [],
   "source": [
    "from classiq import write_qmod\n",
    "\n",
    "write_qmod(qmod, \"min_graph_coloring\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f1a08a1-2ed6-46c6-9083-afd3d8b4e268",
   "metadata": {},
   "source": [
    "## Synthesizing the QAOA Circuit and Solving the Problem\n",
    "\n",
    "We can now synthesize and view the QAOA circuit (ansatz) used to solve the optimization problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3a99384f-c835-44a5-811c-bc69b5c60aae",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:52:37.828100Z",
     "iopub.status.busy": "2024-05-07T15:52:37.827841Z",
     "iopub.status.idle": "2024-05-07T15:53:53.579236Z",
     "shell.execute_reply": "2024-05-07T15:53:53.577934Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Opening: https://platform.classiq.io/circuit/8da93adf-8ec5-44a4-838a-7d1f172c55db?version=0.41.0.dev39%2B79c8fd0855\n"
     ]
    }
   ],
   "source": [
    "from classiq import show, synthesize\n",
    "\n",
    "qprog = synthesize(qmod)\n",
    "show(qprog)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd7640ce-3bed-4d79-97e8-fce32d29e720",
   "metadata": {},
   "source": [
    "We now solve the problem by calling the `execute` function on the quantum program we have generated:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9c5fc0fc-3f9c-457e-9a7f-97d21290c67b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:53:53.583996Z",
     "iopub.status.busy": "2024-05-07T15:53:53.582796Z",
     "iopub.status.idle": "2024-05-07T15:59:25.538607Z",
     "shell.execute_reply": "2024-05-07T15:59:25.537830Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from classiq import execute\n",
    "\n",
    "res = execute(qprog).result()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e7b9756-2703-41ae-a7b6-0ad3ce270330",
   "metadata": {},
   "source": [
    "We can check the convergence of the run:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0d3191c7-ea88-4888-a1b7-aeed6cc65cf2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:25.544008Z",
     "iopub.status.busy": "2024-05-07T15:59:25.542827Z",
     "iopub.status.idle": "2024-05-07T15:59:25.600344Z",
     "shell.execute_reply": "2024-05-07T15:59:25.597759Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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",
      "text/plain": [
       "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=640x480>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from classiq.execution import VQESolverResult\n",
    "\n",
    "vqe_result = res[0].value\n",
    "vqe_result.convergence_graph"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e75fc5d-29fe-4392-a6fb-64a76ca4c0b8",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Optimization Results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6224908a-8b94-4f43-a73f-b647f6bcd56f",
   "metadata": {},
   "source": [
    "We can also examine the statistics of the algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "50ce011c-6ad5-4ef8-b23b-0f009f464bad",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:25.604399Z",
     "iopub.status.busy": "2024-05-07T15:59:25.604039Z",
     "iopub.status.idle": "2024-05-07T15:59:27.456960Z",
     "shell.execute_reply": "2024-05-07T15:59:27.455248Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>probability</th>\n",
       "      <th>cost</th>\n",
       "      <th>solution</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>301</th>\n",
       "      <td>0.001</td>\n",
       "      <td>3.0</td>\n",
       "      <td>[1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>466</th>\n",
       "      <td>0.001</td>\n",
       "      <td>3.0</td>\n",
       "      <td>[0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>734</th>\n",
       "      <td>0.001</td>\n",
       "      <td>12.0</td>\n",
       "      <td>[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>0.002</td>\n",
       "      <td>12.0</td>\n",
       "      <td>[0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1]</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>533</th>\n",
       "      <td>0.001</td>\n",
       "      <td>12.0</td>\n",
       "      <td>[0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0]</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     probability  cost                                       solution  count\n",
       "301        0.001   3.0  [1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0]      1\n",
       "466        0.001   3.0  [0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0]      1\n",
       "734        0.001  12.0  [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1]      1\n",
       "47         0.002  12.0  [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1]      2\n",
       "533        0.001  12.0  [0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0]      1"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "from classiq.applications.combinatorial_optimization import (\n",
    "    get_optimization_solution_from_pyo,\n",
    ")\n",
    "\n",
    "solution = get_optimization_solution_from_pyo(\n",
    "    coloring_model, vqe_result=vqe_result, penalty_energy=qaoa_config.penalty_energy\n",
    ")\n",
    "optimization_result = pd.DataFrame.from_records(solution)\n",
    "optimization_result.sort_values(by=\"cost\", ascending=True).head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc772380-e47e-4ce7-9ed9-c62879911c09",
   "metadata": {},
   "source": [
    "And the histogram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9793d479-62f9-4a4b-92bc-439eb1ef9ba5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:27.461831Z",
     "iopub.status.busy": "2024-05-07T15:59:27.460621Z",
     "iopub.status.idle": "2024-05-07T15:59:27.757270Z",
     "shell.execute_reply": "2024-05-07T15:59:27.756515Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<Axes: title={'center': 'cost'}>]], dtype=object)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "optimization_result.hist(\"cost\", weights=optimization_result[\"probability\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ba86406-7487-449d-a790-0c8fcec11b73",
   "metadata": {},
   "source": [
    "Let us plot the best solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "da924ee8-2a38-470b-9175-37a05c22f7ed",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:27.762214Z",
     "iopub.status.busy": "2024-05-07T15:59:27.761227Z",
     "iopub.status.idle": "2024-05-07T15:59:27.912020Z",
     "shell.execute_reply": "2024-05-07T15:59:27.911357Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "best_solution = optimization_result.solution[optimization_result.cost.idxmin()]\n",
    "\n",
    "one_hot_solution = np.array(best_solution).reshape([max_num_colors, len(graph.nodes)])\n",
    "integer_solution = np.argmax(one_hot_solution, axis=0)\n",
    "nx.draw_kamada_kawai(\n",
    "    graph, with_labels=True, node_color=integer_solution, cmap=plt.cm.rainbow\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df8a97c2-e473-4744-965a-f48a6a383a70",
   "metadata": {},
   "source": [
    "## Classical optimizer results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0e5afa5-f3bb-4770-9d33-f24872a531b6",
   "metadata": {},
   "source": [
    "Lastly, we can compare to the classical solution of the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d964d750-4792-4fa9-b037-089babb25c76",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:27.914604Z",
     "iopub.status.busy": "2024-05-07T15:59:27.914243Z",
     "iopub.status.idle": "2024-05-07T15:59:28.174157Z",
     "shell.execute_reply": "2024-05-07T15:59:28.173443Z"
    },
    "pycharm": {
     "name": "#%%\n"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ERROR: Solver (asl) returned non-zero return code (-11)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ERROR: Solver log: Couenne 0.5.8 -- an Open-Source solver for Mixed Integer\n",
      "    Nonlinear Optimization Mailing list: couenne@list.coin-or.org\n",
      "    Instructions: http://www.coin-or.org/Couenne couenne:\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solver might have not exited normally. Try again\n",
      "Model unknown\n",
      "\n",
      "  Variables:\n",
      "    x : Size=15, Index=x_index\n",
      "        Key    : Lower : Value : Upper : Fixed : Stale : Domain\n",
      "        (0, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "        (0, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "        (1, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "        (2, 0) :     0 :  None :     1 : False :  True : Binary\n",
      "        (2, 1) :     0 :  None :     1 : False :  True : Binary\n",
      "        (2, 2) :     0 :  None :     1 : False :  True : Binary\n",
      "        (2, 3) :     0 :  None :     1 : False :  True : Binary\n",
      "        (2, 4) :     0 :  None :     1 : False :  True : Binary\n",
      "\n",
      "  Objectives:\n",
      "    value : Size=1, Index=None, Active=True\n",
      "ERROR: evaluating object as numeric value: x[0,0]\n",
      "        (object: <class 'pyomo.core.base.var._GeneralVarData'>)\n",
      "    No value for uninitialized NumericValue object x[0,0]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ERROR: evaluating object as numeric value: value\n",
      "        (object: <class 'pyomo.core.base.objective.ScalarObjective'>)\n",
      "    No value for uninitialized NumericValue object x[0,0]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Key : Active : Value\n",
      "        None :   None :  None\n",
      "\n",
      "  Constraints:\n",
      "    conflicting_color_constraint : Size=1\n",
      "        Key  : Lower : Body : Upper\n",
      "        None :   0.0 : None :   0.0\n",
      "    each_vertex_is_colored : Size=5\n",
      "        Key : Lower : Body : Upper\n",
      "          0 :   1.0 : None :   1.0\n",
      "          1 :   1.0 : None :   1.0\n",
      "          2 :   1.0 : None :   1.0\n",
      "          3 :   1.0 : None :   1.0\n",
      "          4 :   1.0 : None :   1.0\n"
     ]
    }
   ],
   "source": [
    "from pyomo.common.errors import ApplicationError\n",
    "from pyomo.opt import SolverFactory\n",
    "\n",
    "solver = SolverFactory(\"couenne\")\n",
    "result = None\n",
    "try:\n",
    "    result = solver.solve(coloring_model)\n",
    "except ApplicationError:\n",
    "    print(\"Solver might have not exited normally. Try again\")\n",
    "\n",
    "coloring_model.display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c356a469-b506-457d-b442-f368be978d13",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-05-07T15:59:28.176765Z",
     "iopub.status.busy": "2024-05-07T15:59:28.176259Z",
     "iopub.status.idle": "2024-05-07T15:59:28.180545Z",
     "shell.execute_reply": "2024-05-07T15:59:28.179974Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "if result:\n",
    "    classical_solution = [\n",
    "        pyo.value(coloring_model.x[i, j])\n",
    "        for i in range(max_num_colors)\n",
    "        for j in range(len(graph.nodes))\n",
    "    ]\n",
    "    one_hot_solution = np.array(classical_solution).reshape(\n",
    "        [max_num_colors, len(graph.nodes)]\n",
    "    )\n",
    "    integer_solution = np.argmax(one_hot_solution, axis=0)\n",
    "    nx.draw_kamada_kawai(\n",
    "        graph, with_labels=True, node_color=integer_solution, cmap=plt.cm.rainbow\n",
    "    )"
   ]
  }
 ],
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